Detergent composition for hard surfaces

ABSTRACT

A detergent composition for hard surfaces is disclosed, which contains: (a) a mixture consisting of at least two compounds represented by formula (I), wherein s is an integer from 1 to 10, representing the number of moles of the ethylene oxide group, which are different in degree of polymerization, said mixture (a) satisfying relationship (1), wherein N t  is the percent by weight of a compound having t mol of the oxyethylene group added based on the weight of mixture (a). The detergent composition has excellent detergency and foaming properties and is useful for removal of denatured oily dirt in the kitchen.

FIELD OF THE INVENTION

This invention relates to a detergent composition for a hard surface andmore particularly a detergent composition having excellent foamingproperties which effectively, safely and rapidly removes clinging dirt,such as greasy dirt on tiles, enameled ironware, etc. in a kitchen thatis the cooking oil splashed during cooking and denatured with heat ortime.

BACKGROUND OF THE INVENTION

A ventilator, a stove, etc. in the kitchen of homes easily get greasywith an oily and sticky substance that is difficult to remove. This oilydirt is denatured cooking oil which has splashed or smoked duringdeep-frying or shallow-frying and stuck to the surface of theventilator, the stove, etc. In general, many kinds of cooking oil have achemical structure containing an unsaturated double bond. Such oileasily undergoes oxidation or polymerization on exposure to air for along time under action of heat or light to gradually increase itsmolecular weight into resinous matter. This is the substance of thedenatured oily dirt which is the cause of difficulty in cleaning thekitchen.

The ventilator in homes, if left uncleaned, gets stained with a notableamount of oily dirt and becomes unsightly in about 6 months. By thattime, the adhered oil has undergone considerable denaturation withstrong adhesion to the substrate, turning into heavy dirt that cannot beeasily removed. Detergent compositions containing an alkylene glycolether type solvent, such as butyl carbitol, have been used for removalof such dirt. However, these detergent compositions were unsatisfactoryfor their ill smell and insufficient detergent action.

In order to solve the above-described problems, Japanese PatentApplication Public Disclosure No. 10808/76 proposes to use hexyleneglycol in combination with an alkylene glycol ether solvent to provide asafe detergent composition which has enhanced detergency and issubstantially odorless.

Further, Japanese Patent Application Public Disclosure No. 236300/89discloses a detergent for hard surfaces which contains a polyoxyalkylenemonobenzyl ether with the number of moles of the polyoxyalkylene addedbeing not more than 5. According to the description of the publication,this detergent lathers nicely.

However, these conventional detergents are still unsatisfactory indetergency for heavy oily dirt, particularly those denatured underinfluences of temperature, humidity, and oxygen.

SUMMARY OF THE INVENTION

Accordingly, an object of the present invention is to provide adetergent composition for hard surfaces (hereinafter simply referred toas hard surface detergent composition) which is excellent in swellingproperties and detergency for heavy dirt, such as oil denatured underinfluences of temperature, humidity, oxygen, etc., and is capable ofrapid cleansing.

As a result of extensive investigations, the present inventors havefound that the above object of the present invention is accomplished bya detergent composition containing a mixture consisting of at least twopolyoxyethylene monophenyl ethers different in degree of polymerizationat a specific mixing ratio. The present invention has been completedbased on this finding.

The present invention provides a hard surface detergent compositioncontaining (a) a mixture consisting of at least two compoundsrepresented by formula (I): ##STR2## wherein s is an integer of from 1to 10, representing the number of moles of the ethylene oxide group,which are different in degree of polymerization, the mixture satisfyingrelationship (1): ##EQU1## wherein Nt is the percent by weight of acompound having t mol of the oxyethylene group added based on the weightof mixture (a).

DETAILED DESCRIPTION OF THE INVENTION

The hard surface detergent composition of the present invention will beillustrated below in greater detail.

The compounds represented by formula (I) which constitute component (a)are polyoxyethylene monophenyl ethers. Component (a) is a mixture of atleast two polyoxyethylene monophenyl ethers different in degree ofpolymerization. From the standpoint of swelling or dissolving action onoily dirt, particularly denatured oily dirt, component (a) shouldsatisfy relationship (1),preferably relationship (2), still preferablyrelationship (3),yet preferably relationship (4), and most preferablyrelationship (5): ##EQU2## wherein Nt is the percent by weight of acompound having t mol of the oxyethylene group added based on the weightof mixture (a) (hereinafter the same). ##EQU3##

Further, it is preferable that component (a) satisfying relationship(2), (3), (4) or (5) satisfies relationship (6): ##EQU4##

The process for preparing component (a) is not particularly limited. Forexample, component (a) can be obtained by a process comprisingarbitrarily selecting at least one compound of formula (I) in which s isbetween 1 and 3 and at least one compound of formula (I) in which s isbetween 4 and 10, preferably between 4 and 6, and mixing them togetherat such a ratio that satisfies any of relationships (1) to (5), or aprocess comprising reacting phenol with ethylene oxide in the presenceof an alkali catalyst, such as sodium hydroxide or potassium hydroxide.

Component (a) is a mixture of at least two of the above-mentionedpolyoxyethylene monophenyl ethers, the two having different degrees ofpolymerization. While a single compound of formula (I) in which s isfrom 1 to 3 or from 4 to 10 is expected to exhibit detergent effects onoily dirt or slightly denatured oily dirt, the action of swelling anddissolving denatured oil can be accelerated by mixing a compound inwhich s is from 1 to 3 and a compound in which s is from 4 to 10,preferably from 4 to 6, at a specific ratio satisfying any of therelationships (1) to (5).

It is preferable that the detergent composition of the present inventionfurther contains (b) an alkali agent (hereinafter referred to ascomponent (b)).

While not limiting, the alkali agent as component (b) preferablyincludes ammonia and alkanolamines. In particular, monoethanolamine anddiethanolamine are preferred for their hydrolytic action on denaturedoil, leading enhanced detergency. These alkali agents may be used eitherindividually or in combination of two or more thereof.

Components (a) and (b) are preferably used at a weight ratio of1/10≦(b)/(a)≦10/1, particularly 1/10≦(b)/(a)≦1/1. If the ratio (b)/(a)is less than 1/10, the effect of addition of component (b) isinsubstantial. A (b)/(a) ratio greater than 10/1 is uneconomical; fordetergency reaches saturation.

If is also preferable that the detergent composition furthermorecontains (c) a surface active agent (hereinafter referred to ascomponent (c)). Component (c) imparts satisfactory detergency andfoaming properties to the detergent composition. In particular, when thedetergent composition is applied by spraying or with a squeeze foamer,component (c) markedly improves retention of the composition, therebysynergistically increasing the swelling action of component (a) ondenatured oily dirt.

While not limiting, component (c) preferably includes the followingnonionic, amphoteric or anionic surface active agents.

From the viewpoint of detergency, foaming properties, and lowirritation, suitable nonionic surface active agents includepolyoxyethylene alkyl ethers, polyoxyethylene alkenyl ethers, higherfatty acid alkanolamides, polyoxyethylene higher fatty acidalkanolamides, amine oxides, and alkyl glycosides, with alkyl glycosidesbeing especially preferred. Specific examples of the nonionic surfaceactive agents are polyoxyethylene(p=3) lauryl ether, polyoxyethylene(p=7) lauryl ether, polyoxyethylene(p=12) lauryl ether, dodecylmaltoside, coconut oil fatty acid diethanolamide, polyoxyethylene(p=2)coconut oil fatty acid monoethanolamide, and lauryldimethylamine oxide(p represents an average degree of polymerization). These nonionicsurface active agents may be used either individually or in combinationof two or more thereof.

From the standpoint of detergency and foaming properties, suitableamphoteric surface active agents include alkylamidocarbobetaines andalkylamidosulfobetaines. Specific examples arelauramidopropyl-N,N-dimethyl-acetic acid betaine,myristamidopropyl-N,N-dimethyl-acetic acid betaine, andcocoamidopropyl-N,N-dimethyl-acetic acid betaine. These amphotericsurface active agents may be used either individually or in combinationof two or more thereof.

Suitable anionic surface active agents include alkylbenzenesulfonates,alkylene oxide-added alkyl or alkenyl ether sulfates, olefinsulfonates,alkanesulfonates, saturated or unsaturated fatty acid salts, alkyleneoxide-added alkyl or alkenyl ether carboxylates, and α-sulfofatty acidsalts or esters. The counter ions forming these salts include alkalimetal ions, e.g., a sodium ion and a potassium ion, an ammonium ion, andalkanolammonium ions, e.g., a monoethanolammonium ion, adiethanolammonium ion and a triethanolammonium ion. The anionic surfaceactive agents may be used either individually or in combination of twoor more thereof.

The nonionic, amphoteric and anionic surface active agents may be usedeither individually or in combination thereof.

Of the above-enumerated surface active agents as component (c),preferred are nonionic surface active agents or amphoteric surfaceactive agents, and particularly nonionic surface active agents, withalkyl glyco-sides being most preferred, for their detergency fordenatured oily dirt.

The alkyl glycosides which can be used as component (c) preferablyinclude those represented by formula (II):

    R.sub.2 (OR.sub.3).sub.x G.sub.y                           (II)

wherein R₂ represents an alkyl group, an alkenyl group or an alkylphenylgroup each having from 8 to 18 carbon atoms, the alkyl moiety of whichmay be straight or branched; R₃ represents an alkylene group having from2 to 4 carbon atoms; G represents a residue of a reducing sugar havingfrom 5 to 7 carbon atoms, such as glucose; x represents a number of from0 to 5 in average; and y represents a number of from 1 to 10 in average.

Water solubility and crystallinity of the alkyl glycoside can beadjusted by varying x in formula (II) between 0 and 5 in average. x ispreferably from 0 to 2, still preferably 0. Where y in formula (II) isgreater than 1 in average, the sugar chains may be bonded through a 1-2bond, a 1-3 bond, a 1-4 bond or a 1-6 bond or an α- or β-pyranoside orfuranoside linkage or a mixture thereof. y is preferably from 1 to 10,still preferably from 1 to 1.5, yet preferably from 1.1 to 1.4. y can bemeasured by proton NMR.

R₂ in formula (II) is preferably an alkyl group having from 10 to 14carbon atoms from the standpoint of solubility and detergency. R₃ ispreferably an alkylene group having 2 or 3 carbon atoms from thestandpoint of water solubility. The structure of G is decided by thestarting mono-, di- or polysaccharide. The starting material for Gpreferably includes glucose and fructose as a monosaccharide and maltoseand sucrose as a di- or polysaccharide from the standpoint ofavailability and cost. Glucose is particularly preferred for itsavailability.

Where an alkyl glycoside (hereinafter referred to as component (c-1)) isused, it is recommended to use it in combination with an amphotericsurface active agent (hereinafter referred to as component (c-2)),preferably an alkylamidocarbobetaine, for improving the quality oflather, such as foaming properties and foam stability. In this case,components (c-1) and (c-2) are preferably used at a (c-1)/(c-2) weightratio of 1/10 or higher for detergency and not higher than 10/1 forfoaming properties, still preferably from 1/8 to 8/1, and yet preferablyfrom 1/5 to 5/1.

It is preferable that components (c) and (b) are used at a (c)/(b)weight ratio of from 1/10 to 10/1, particularly from 1/10 to 1/1. Ifthat ratio is smaller than 1/10, the effect of improving detergency isinsubstantial. The (c)/(b) ratio exceeding 10/1 is uneconomical.

The hard surface detergent composition according to the presentinvention is prepared in a usual manner by mixing the essentialcomponent (a), preferably components (a) and (b), still preferablycomponents (a), (b), and (c-1), yet preferably components (a), (b),(c-1), and (c-2), with water (hereinafter referred to as component (d)),if desired together with other optional components hereinafterdescribed, to obtain an aqueous solution.

Component (a) is used in a proportion of from 0.1 to 30 parts by weight,preferably from 1 to 20 parts by weight, still preferably from 3 to 15parts by weight, per 100 parts by weight of the total weight ofcomponents (a) to (d). If the proportion of component (a) is less than0.1 part, sufficient detergency cannot be obtained. A proportion ofhigher than 30 parts, at which the effects reach saturation, isuneconomical.

Component (b) is used at a proportion of from 0.01 to 20 parts byweight, preferably from 0.05 to 10 parts by weight, per 100 parts byweight of the total weight of components (a) to (d). If the proportionof component (b) is less than 0.01 part, the detergency tends to beinsufficient. A proportion of higher than 20 parts, at which the effectsreach saturation, is uneconomical.

Component (c) is used in a proportion of from 0.1 to 20 parts by weight,preferably from 0.1 to 15 parts by weight, more preferably from 1 to 10parts by weight, per 100 parts by weight of the total weight ofcomponents (a) to (d). If the proportion of component (c) is less than0.1 part, the detergency tends to be insufficient. A proportion higherthan 20 parts, at which the effects reach saturation, is uneconomical.

Component (d) is preferably used at a proportion of from 30 to 99.5parts by weight, still preferably from 75 to 95 parts by weight.

If desired, the hard surface detergent composition of the presentinvention may contain other optional components, such as a sequesteringagent, a low-temperature stabilizer, a viscosity modifier, and the like.

Any of commonly employed sequestering agents may be used in the presentinvention without restriction. Suitable sequestering agents includehydroxycarboxylic acids, e.g., citric acid and malic acid; condensedphosphoric acids, e.g., pyrophosphoric acid; aminocarboxylic acids,e.g., ethylenediaminetetraacetic acid and hydroxyethylenediamineaceticacid; and alkali meal (Na or K) salts, ammonium salts or alkanolaminesalts thereof and their water-soluble salts. These sequestering agentsmay be used either individually or in combination of two or morethereof. The sequestering agent is used in an amount of from 0.001 to 20parts by weight per 100 parts by weight of the total weight ofcomponents (a) to (d).

Useful low-temperature stabilizers include lower alcohols, e.g., ethylalcohol; lower glycols, e.g., ethylene glycol; and loweralkylbenzenesulfonates, e.g., benzenesulfonates and toluenesulfonates.The low-temperature stabilizer is usually used in an amount of from 0.1to 20 parts by weight per 100 parts by weight of the total weight ofcomponents (a) to (d).

Useful viscosity modifiers include smectites, acrylic homo- orcopolymers, such as sodium polyacrylate, cross-linked polyacrylic acids,and polyalkyl acrylates, polyvinyl alcohol, hydroxyethyl cellulose,carboxymethyl cellulose, polyvinyl pyrrolidone, and maleic anhydridepolymers. The viscosity modifier is used in an amount of from 0.1 to 10parts by weight per 100 parts by weight of the total weight ofcomponents (a) to (d).

In order to enhance the commercial value of the detergent composition,the composition may further contain perfumes, colorants, antiseptics,antioxidants, thickeners, and so on.

The hard surface detergent composition according to the presentinvention can be used, for example, by bringing dirt into contact withthe composition for 5 to 30 minutes by, for example, soaking andremoving the thus released and floated dirt. The contact time may beextended to 5 to 10 hours for heavy dirt. Where the composition isapplied to a slanted or vertical surface, the detergent composition maybe foamed and sprayed thereto to assure retention on the surface.

The present invention will now be illustrated in greater detail withreference to Examples in view of Comparative Examples, but it should beunderstood that the present invention is not deemed to be limitedthereto.

EXAMPLES 1 AND COMPARATIVE EXAMPLES 1 TO 7

A detergent composition having the composition shown in Table 1 below(unit: wt %) was prepared and subjected to a swelling test in accordancewith the following test method. The results obtained are shown in Table1.

Swelling Test:

Fourteen milligrams of rapeseed oil were baked on a Teflon-coated plateat 180° C. for 10 hours to prepare a denatured oil cake. The denaturedoil cake was soaked in 2 ml of the detergent composition for 5 hours,and the swell (Q) of the cake was obtained as follows. ##EQU5## whereinD_(p) is a density of a denatured oil; D_(s) is a density of a detergentcomposition; W_(a) is a weight of a non-treated denatured oil; and W_(b)is a weight of a swollen denatured oil.

                                      TABLE 1                                     __________________________________________________________________________                        Example                                                                            Comparative Example No.                                                  1    1  2  3  4  5  6  7                                  __________________________________________________________________________     ##STR3##           10                                                         ##STR4##                10                                                    ##STR5##                   10                                                 ##STR6##                      10                                              ##STR7##                         10                                           ##STR8##                            10                                        ##STR9##                               10                                    Butyl carbitol                             10                                 Polyoxyethylene     2    2  2  2  2  2  2  2                                  (p*8 = 7) lauryl ether                                                        Monoethanolamine    5    5  5  5  5  5  5  5                                  Water               bal.*9                                                                             bal.                                                                             bal.                                                                             bal.                                                                             bal.                                                                             bal.                                                                             bal.                                                                             bal.                               Swell (Q)           4.4  2.7                                                                              3.6                                                                              3.3                                                                              3.2                                                                              3.2                                                                              2.9                                                                              2.5                                __________________________________________________________________________     Note:                                                                         *1: A mixture having the following ethylene oxide (EO) distribution: EO 1     mol = 4 wt %; EO 2 mol = 27 wt %; EO 3 mol = 32 wt %; EO 4 mol = 22 wt %;     EO 5 mol = 11 wt %; EO 6 mol = 4 wt %                                         *2: Commercially available reagent of first grade, produced by Kanto          Chemical Co., Ltd.                                                            *3: Hisolve DHP, produced by Toho Chemical Industry Co., Ltd.                 *4 and *5: Obtained by adding ethylene oxide to phenol and purified by        distillation.                                                                 *6: Synthesized by tosylating the hydroxyl group of the compound wherein      = 2 and reacting it with HOCH.sub.2 CH.sub.2 OCH.sub.2 CH.sub.2 OCH.sub.2     CH.sub.2 OH by refluxing in dioxane in the presence of sodium hydroxide.      *7: Synthesized by tosylating the hydroxyl group of the compound wherein      = 2 and reacting it with HOCH.sub.2 CH.sub.2 OCH.sub.2 CH.sub.2 OCH.sub.2     CH.sub.2 OCH.sub.2 CH.sub.2 OH by refluxing in dioxane in the presence of     sodium hydroxide.                                                             *8: Average degree of polymerization.                                         *9: Balance                                                              

EXAMPLES 2 TO 4 AND COMPARATIVE EXAMPLES 8 TO 9

A detergent composition having the composition shown in Table 2 below(unit: wt %) was prepared and subjected to a swelling test in the samemanner as in Example 1. Further, the detergency and foaming propertiesof the composition were evaluated according to the following testmethods. The results obtained are shown in Table 2.

Detergency Test:

Frying oil was uniformly applied to an iron plate and baked at 180° C.for 10 hours to prepare a plate with an almost dried film as a dirtmodel for a detergency test. The detergent composition was dropped onthe vertically set plate with a dirt model and allowed to stand for 40seconds. The released and floated dirt was lightly wiped off withabsorbent wadding, and the degree of cleansing (detergency) was observedwith the naked eye and rated according to the following standard.

A . . . The dirt was completely removed.

B . . . About 80% of the dirt was removed.

C . . . About 60% of the dirt was removed.

D . . . About 50% of the dirt was removed.

E . . . About 30% of the dirt was removed.

F . . . Dirt was not removed at all.

Test of Foaming Properties:

The detergent composition was sprayed onto a window-pane by means of acommercially available sprayer. The lather formed on spraying wasvisually observed and rated as follows.

A . . . Good lather.

B . . . Slight lather.

C . . . No lather.

                  TABLE 2                                                         ______________________________________                                                 Ex    Ex-     Ex-     Compara.                                                                             Compara.                                         ample ample   ample   Example                                                                              Example                                          2     3       4       8      9                                       ______________________________________                                        Component (a):                                                                Formula (I)*1:                                                                S*2        6.6     7.5     8.1          0.7                                   N*3        3.4     2.5     1.9          9.3                                   Component (b):                                                                Monoethanolamine                                                                         5               5     5                                            Diethanolamine     5                    5                                     Component (c):                                                                Polyoxyethylene                  3                                            lauryl ether                                                                  (p*4 = 3)                                                                     Dodecyl maltoside                                                                        3       5                                                          Lauryldimethyl-                                                                          1                                                                  amine oxide                                                                   Sodium lauryl-             3                                                  benzenesulfonate                                                              Sodium stearyl-                         5                                     sulfate                                                                       Ethanol                          10                                           Water      bal.*5  bal.    bal.  bal.   bal.                                  Evaluation:                                                                   Detergency A       A       B     F      C                                     Foaming    A       A       A     C      B                                     Properties                                                                    Swell (Q)  4.8     4.5     4.1   2.0    3.0                                   ______________________________________                                         Note:                                                                         *1: A mixture having ethylene oxide distribution shown in Table 3.            ##STR10##                                                                     ##STR11##                                                                     *4: Average degree of polymerization.                                         *5: Balance                                                              

                  TABLE 3                                                         ______________________________________                                                                   Comparative                                                        Example No.                                                                              Example No.                                                        2    3      4      8    9                                     ______________________________________                                         ##STR12##        1.29   1.56   1.9                                            ##STR13##        1.7    2.04   4.2                                            ##STR14##        3.61   3.9    2.0       0.7                                  ##STR15##        1.82   1.6    1.01      2.25                                 ##STR16##        0.98   0.7    0.89      6.2                                  ##STR17##        0.6    0.2              0.85                                ______________________________________                                    

It can be seen from the above results that the hard surface detergentcomposition of the present invention is excellent in swelling propertiesand detergency for oily dirt. In addition, the hard surface detergentcomposition was proved capable of rapid cleansing.

As described and demonstrated above, the hard surface detergentcomposition comprising component (a) has excellent swelling propertiesand detergent action on dirt difficult to remove, such as oil havingdenatured under the influences of temperature, humidity, oxygen, etc.and is capable of rapid cleansing.

In particular, the hard surface detergent composition comprisingcomponents (a) to (d) at a specific ratio shows further improvements.

The hard surface detergent composition of the present invention isparticularly useful for removing denatured oily dirt.

While the invention has been described in detail and with reference tospecific examples thereof, it will be apparent to one skilled in the artthat various changes and modifications can be made therein withoutdeparting from the spirit and scope thereof.

We claim:
 1. A detergent composition for hard surfaces containing(a) 0.1to 30 parts by weight of a mixture consisting of compounds representedby formula (I) : ##STR18## wherein s is an integer of from 1 to 10,representing the number of moles of the ethylene oxide group, which aredifferent in degree of polymerization, said mixture (a) satisfyingrelationship (1): ##EQU6## wherein N_(t) is the percent by weight of acompound having t mol of the oxyethylene group added based on the weightof mixture (a), (b) 0.01 to 20 parts by weight of ammonia or analkanolamine, and (c) 0.1 to 20 parts by weight of a surface activeagent selected from the group consisting of an alkyl glycoside and anamine oxide; and wherein the said component (a) mixture of compoundscontain ethoxylated phenols having mole numbers of addition of 4, 5 and6.
 2. A detergent composition for hard surfaces containing (a) from 0.1to 30 parts by weight of a mixture consisting of compounds representedby formula (I): ##STR19## wherein s is an integer of from 1 to 10,representing the number of moles of the ethylene oxide group, which aredifferent in degree of polymerization, said mixture (a) satisfyingrelationship (1): ##EQU7## wherein N_(t) is the percent by weight of acompound having t mol of the oxyethylene group added based on the weightof mixture (a), (b) from 0.01 to 20 parts by weight of an alkali agent,(c) from 0.1 to 20 parts by weight of at least one surface active agentselected from the group consisting of an alkyl glycoside and an amineoxide, and (d) water, each per 100 parts by weight of the total weightof components (a) to (d).
 3. A detergent composition for hard surfacesas claimed in claim 2, wherein said detergent composition is for removalof denatured oily dirt.
 4. A method for removing denatured oily dirt onhard surfaces using a detergent composition for hard surfaces claimed inclaim
 2. 5. The composition according to claim 1 wherein said alkylglycoside is represented by the formula:

    R.sub.2 (OR.sub.3).sub.x G.sub.y                           (II)

wherein R₂ represents an alkyl group, an alkenyl group or an alkylphenylgroup each having from 8 to 18 carbon atoms, the alkyl moiety of whichmay be straight or branched; R₃ represents an alkylene group having form2 to 4 carbon atoms; G represents a residue or a reducing sugar havingfrom 5 to 7 carbon atoms; x represents a number of from 0 to 5 on theaverage; and y represents a number of from 1 to 10 on the average. 6.The composition according to claim 2 wherein said alkyl glycoside isrepresented by the formula:

    R.sub.2 (OR.sub.3).sub.x G.sub.y                           (II)

wherein R₂ represents an alkyl group, an alkenyl group or an alkylphenylgroup each having from 8 to 18 carbon atoms, the alkyl moiety of whichmay be straight or branched; R₃ represents an alkylene group having form2 to 4 carbon atoms; G represents a residue or a reducing sugar havingfrom 5 to 7 carbon atoms; x represents a number of from 0 to 5 on theaverage; and y represents a number of from 1 to 10 on the average.